   Chapter 9, Problem 9.52E

Chapter
Section
Textbook Problem

# (a) Compare equations 9.31 , 9.34 , and 9.41 and propose a formula for the radius of a hydrogen-like atom that has atomic charge Z . (b) What is the radius of a U 91 + ion if the electron has a quantum number of 100 ? Ignore any possible relativistic effects.

Interpretation Introduction

(a)

Interpretation:

The formula for the radius of a hydrogen-like atom that has atomic charge Z is to be stated.

Concept introduction:

The radius of a hydrogen atom that has a particular value of principal quantum number n can be predicted using Bohr’s assumption for atomic model. The relation is given as follows.

r=εon2h2πmee2

Explanation

Equation 9.31 is given below.

Etotal=12e24πεor

Equation 9.34 is given below.

r=εon2h2πmee2

Equation 9.41 is given below.

Etotal=Z2mee48εo2n2h2

Calculate the value of r from equation 9.31 as follows.

Etotal=12e24πεorr=12e24πεoEtotal

Substitute the value of Etotal from equation 9

Interpretation Introduction

(b)

Interpretation:

The radius of U91+ ion if the electron has a quantum number of 100 is to be calculated.

Concept introduction:

The radius of a hydrogen atom that has a particular value of principal quantum number n can be predicted using Bohr’s assumption for atomic model. The relation is given as follows.

r=εon2h2πmee2

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